On the shore singularity of waterwave theory. Part 2. Small waves don't break on gentle beaches
Abstract
The model of gravitational surface waves on beaches of small slope formulated in and its mathematical theory are used to show how an incidentwave amplitude can be defined so that a bound on it guarantees solutions which respect the assumptions of the model everywhere and forever. The structure of those solutions far from shore is then compared with that predicted near shore by the classical, linear theory to remove the indeterminacies of both theories: Shore reflection is determined for the classical theory, and it is shown how the critical length scale and amplitude of the beach theory are related to the familiar wavelength and amplitude in deep water. These results indicate that the beach theory captures and elucidates the basic singularity structure underlying the shore behavior of gravitational surface waves.
 Publication:

Technical Summary Report Wisconsin Univ
 Pub Date:
 October 1985
 Bibcode:
 1985wisc.reptV....M
 Keywords:

 Beaches;
 Gravity Waves;
 Mathematical Models;
 Prediction Analysis Techniques;
 Surface Waves;
 Water Waves;
 Amplitudes;
 Erosion;
 Linearity;
 Ocean Models;
 Shorelines;
 Slopes;
 Water Depth;
 Fluid Mechanics and Heat Transfer